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Modeling Transition Metal Alloys

Wilkins group developing methods to design, engineer new materials

Wilkins’ research group investigated key components in many technologically important alloys, constructing inter-atomic potentials that are accurate and reliable under a wide range of pressures and temperatures.

Developing new materials and engineering their novel properties have been the driving forces behind many revolutionary modern technologies. The emerging capabilities in predictive modeling and simulation have created an opportunity to implement the “materials-by-design” paradigm.

A research group at The Ohio State University has been developing a systematic way to design accurate empirical inter-atomic potentials for many technologically important metals and metal alloys. While quantum mechanical simulations are usually highly accurate and reliable, they are computationally expensive. Atomistic molecular dynamics simulations based on classical inter-atomic potentials, though, are much less computationally demanding and extend materials simulations beyond the reach of quantum mechanical simulations.

“Vital to the success of classical atomistic simulations are high-quality potentials capable of mimicking the quantum mechanical interactions between atoms,” said John Wilkins, Ph.D., Ohio Eminent Scholar and Ohio State professor of physics. “To bridge between accurate quantum mechanical interactions and fast classical potentials, we optimize the parameters of classical potentials to forces, energies and stresses computed by quantum mechanical simulations for representative atomic configurations.”

His research team leverages the embedded-atom method potential and its expanded versions as the formats for the potentials.

“What is unique about our group’s approach is that we use ‘splines’ to represent functional terms of potential,” said Hyoungki Park, Ph.D., a postdoctoral researcher on the team. “Splines are piecewise polynomials that have a high degree of smoothness at their connection points, which are called spline knots.”

Discretization of functional terms in the potential by spline knots yields a large number of parameters, and connecting these spline knots forms a hypersurface. The researchers “tame/train” the hypersurface by fitting it to a quantum mechanical database. Developing complex spline-based potentials by finding a global minimum fit to large quantum mechanical databases has been too difficult for publicly available optimizers.

Utilizing Ohio Supercomputer Center systems, the team built a robust optimizer that uses a hybrid combination of the genetic algorithm and a least-squares minimization routine.

The researchers have constructed many inter-
atomic potentials for vanadium, niobium, tantalum, molybdenum and tungsten. These potentials are accurate and reliable under a wide range of pressures and temperatures, making them very useful for studying mechanical and thermodynamic behaviors.